I have a Pearl 902-C double bass pedal. It has worked well as a beginner double pedal as I've been getting better and better at double bass. The pedal is going on only two years old but something just doesn't feel right while I've been playing recently. I like playing with medium tension. However, when I have the pedals set from anywhere from small to medium tension, the pedals seem to "mis-hit". What I mean by this is the actual pedal feels very loose and shakes from side to side slightly instead of just up and down. Does something in the pedal need to be replaced? I have the pedal set to a really high tension now so the side shaking isn't as effective but it's crazy tiring!

Something is loose. You can't wear out even the cheapest pedal, drumming is not such a demanding activity for a piece of steel... I think.
Take it off, put it in the light on the kitchen table and you will see. :)

Could be a set screw has come loose somewhere, like in one of the universal joints. Something is slipping somewhere. Make sure your connecting rod is tight between the pedals, especially if it has two screws at each end. Could be the screws are loose for the width adjustment, too, and the bar is sliding in and out?

If the foot board is what is moving, check the screw that holds the foot plate in place. If I am correct, your pedal allows for moving the foot board forward or back. If this screw is loose, the foot board will pivot from side to side at this screw. If not the screw, check the hinge where the plate and board connect. These have been known to wear out after time.

If it is more than the foot board moving, start checking screws everywhere. I would start with the spring perch, since you said higher tension helps. If the perch screw is loose, the shaft could be possibly moving side to side between the bearings. Check the cam screw. If it is loose, it can potentially move laterally on the shaft, torquing the chain, thus pulling on the foot board. A loose cam can also have enough play in it to explain those misses you are experiencing.

Without actually seeing it (make a video, hint hint) or getting my hands on it, there is no way to tell for sure what the problem is.

On a closer examination, it seems most of the problem was because my bass drum was not leveled so the pedals would hit at around 90 degrees. It was leaning forward and I'm not even sure how because I didn't adjust anything, but it made the angle probably about 100 degrees, definitely enough to mess with footwork I'd say.

Took a look at the pedals but other than the pedalboards being insanely dirty, everything seemed secure and nothing was out of the ordinary.